The Tesla coil is an instrument that can step up voltages to high voltages at high frequencies.

Tesla worked with alternating current  energy moving back and forth. He worked with low frequencies at Niagara Falls  60 cycles per second. But he needed to have high voltage at high frequencies to do his experiments with wireless transmission  60,000 cycles per second and higher.

He realized that James Clerk Maxwell predicted that waves could propagate with antennas. In order to do this, he needed to build equipment to make high-frequency currents.

So if you want to talk about the genius of the Tesla coil, I think it is couched in Tesla's dreams and visions of the work he was going to do.

Tesla was a man who understood what no other scientist of the time understood  he understood electrical resonance. He understood the idea that energy passed back and forth in an electrical system.

The Tesla coil as we know it in the 1890s is a very good example of a resonant system, using low kilohertz and a double tuned circuit so energy can be transferred between two systems  that essentially transmits a radio signal.

Radio

If you want to get a radio signal to radiate into the atmosphere, you want it to travel through the air strong enough to detect as a voltage.

So in that way alone, Tesla created a system of tuned circuits that he would cause waves from an antenna system to radiate out into the atmosphere. Therefore, Tesla's system was the one that made radio possible.

Marconi

Marconi used Hertz's system initially, but sending the signal "S" across the Atlantic would not have been possible with that system. So it became obvious to Marconi and other experimenters of the time that Tesla's system was an efficient, powerful resonator that produced waves you could work with.

The simple fact about Marconi's "S" is that he used the Tesla system to transmit signals and claimed that these were ideas he had developed himself.

At the Marconi site on Cape Cod, the placards state clearly that Marconi used the Tesla oscillator to send signals.

Marconi was a good businessman. He built the first practical equipment. And for that reason, his name is the one people remember when they think of radio.

Tesla The Visionary

Tesla was a visionary genius. There aren't many of them. And he was willing to give his life to his visions. And for that reason he probed deeply into the secrets of nature and gave us the contributions that he did.